Multiple file browsers (different files) using python
If I understand your question clearly, you want to proceed with the first modal result and run the second operator right?
Instead of calling two modal operator, you should call the second one in the first operator &quot;execute&quot; function. In that block, the modal part is done and can call another modal operator.
A simple snippet that run two file select window in a sequence:
import bpy
from bpy_extras.io_utils import ExportHelper

class ExportCommon(bpy.types.Operator, ExportHelper):

    bl_idname = &quot;export.common&quot;
    bl_label = &quot;Export common&quot;
    filename: bpy.props.StringProperty()
    filename_ext = &quot;.fbx&quot;

    def invoke(self, context, event):  
        context.window_manager.fileselect_add(self)
        return {'RUNNING_MODAL'}

    def execute(self, context):
        print(self.filename)
        bpy.ops.wm.save_as_mainfile('INVOKE_DEFAULT', copy=True)
        return {&quot;FINISHED&quot;}

bpy.utils.register_class(ExportCommon)

bpy.ops.export.common('INVOKE_DEFAULT')